step-44: Finite strain elasticity
The objective of this tutorial is to demonstrate one approach to modelling the
deformation of a nearly-incompressible elastic solid.
The elastic response is governed by a non-linear, hyperelastic free-energy
function.
The geometrical response is also nonlinear, i.e. we consider finite
deformations.
Thus, the tutorial aims to introduce key concepts in nonlinear continuum
mechanics and provides a starting point for people who wish to use deal.II in
solid mechanics.
Modelling of nearly-incompressible elastic materials is challenging for at
least two reasons.
The first is that standard displacement-based elasticity formulations exhibit
locking behaviour.
This completely ruins the convergence behaviour associated with the finite
element method.
The second challenge is choosing an effective strategy to combat locking; there
are many.
We've chosen a three-field formulation wherein the displacement, pressure and
dilatation (volume change) are the independent primary fields.
The model can easily be stripped down to a standard single-field approach if
you are not concerned about locking.
Alternatively, it could easily be extended to the fully-incompressible case.
Jean-Paul Pelteret and Andrew McBride
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